322 research outputs found
Dynamical variety of shapes in financial multifractality
The concept of multifractality offers a powerful formal tool to filter out
multitude of the most relevant characteristics of complex time series. The
related studies thus far presented in the scientific literature typically limit
themselves to evaluation of whether or not a time series is multifractal and
width of the resulting singularity spectrum is considered a measure of the
degree of complexity involved. However, the character of the complexity of time
series generated by the natural processes usually appears much more intricate
than such a bare statement can reflect. As an example, based on the long-term
records of S&P500 and NASDAQ - the two world leading stock market indices - the
present study shows that they indeed develop the multifractal features, but
these features evolve through a variety of shapes, most often strongly
asymmetric, whose changes typically are correlated with the historically most
significant events experienced by the world economy. Relating at the same time
the index multifractal singularity spectra to those of the component stocks
that form this index reflects the varying degree of correlations involved among
the stocks.Comment: 26 pages, 10 figure
Quantifying origin and character of long-range correlations in narrative texts
In natural language using short sentences is considered efficient for
communication. However, a text composed exclusively of such sentences looks
technical and reads boring. A text composed of long ones, on the other hand,
demands significantly more effort for comprehension. Studying characteristics
of the sentence length variability (SLV) in a large corpus of world-famous
literary texts shows that an appealing and aesthetic optimum appears somewhere
in between and involves selfsimilar, cascade-like alternation of various
lengths sentences. A related quantitative observation is that the power spectra
S(f) of thus characterized SLV universally develop a convincing `1/f^beta'
scaling with the average exponent beta =~ 1/2, close to what has been
identified before in musical compositions or in the brain waves. An
overwhelming majority of the studied texts simply obeys such fractal attributes
but especially spectacular in this respect are hypertext-like, "stream of
consciousness" novels. In addition, they appear to develop structures
characteristic of irreducibly interwoven sets of fractals called multifractals.
Scaling of S(f) in the present context implies existence of the long-range
correlations in texts and appearance of multifractality indicates that they
carry even a nonlinear component. A distinct role of the full stops in inducing
the long-range correlations in texts is evidenced by the fact that the above
quantitative characteristics on the long-range correlations manifest themselves
in variation of the full stops recurrence times along texts, thus in SLV, but
to a much lesser degree in the recurrence times of the most frequent words. In
this latter case the nonlinear correlations, thus multifractality, disappear
even completely for all the texts considered. Treated as one extra word, the
full stops at the same time appear to obey the Zipfian rank-frequency
distribution, however.Comment: 28 pages, 8 figures, accepted for publication in Information Science
Exploitation of Memetics for Melodic Sequences Generation
Music, or in narrower sense, melodic contours of the aesthetically arranged pitches and the respective durations attracts our cognition since the beginning and now shaping the way we think in the complex life of culture. From evolutionary school of thoughts we could learn our perspective of seeing the musical diversity of folk songs in Indonesian archipelago by hypothesizing the aligning memes throughout the data sets. By regarding the memeplexes constructed from the the Zipf-Mandelbrot Law in melodic sequences and some mathematical characteristics of songs e.g.: gyration and spiraling effect, we construct evolutionary steps i.e.: genetic algorithm as tools for generating melodic sequences as an alternating computational methods to model the cognitive processes creating songs. While we build a melodic-contour generator, we present the enrichment on seeing the roles of limitless landscape of creativity and innovation guided by particular inspirations in the creation of work of art in general
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
On Multifractal Structure in Non-Representational Art
Multifractal analysis techniques are applied to patterns in several abstract
expressionist artworks, paintined by various artists. The analysis is carried
out on two distinct types of structures: the physical patterns formed by a
specific color (``blobs''), as well as patterns formed by the luminance
gradient between adjacent colors (``edges''). It is found that the analysis
method applied to ``blobs'' cannot distinguish between artists of the same
movement, yielding a multifractal spectrum of dimensions between about 1.5-1.8.
The method can distinguish between different types of images, however, as
demonstrated by studying a radically different type of art. The data suggests
that the ``edge'' method can distinguish between artists in the same movement,
and is proposed to represent a toy model of visual discrimination. A ``fractal
reconstruction'' analysis technique is also applied to the images, in order to
determine whether or not a specific signature can be extracted which might
serve as a type of fingerprint for the movement. However, these results are
vague and no direct conclusions may be drawn.Comment: 53 pp LaTeX, 10 figures (ps/eps
An Alternative Postulate to see Melody as “Language”
The paper proposes a way to see melodic features in music/songs in the terms of “letters” constituting “words”, while in return investigating the fulfillment of Zipf-Mandelbrot Law in them. Some interesting findings are reported including some possible conjectures for classification of melodic and musical artifacts considering several aspects of culture. The paper ends with some discussions related to further directions, be it enrichment in musicology and the possible plan for musical generative art
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